Fall09MT2b

# Fall09MT2b - 1 Economics 420K(Microeconomic Theory Second...

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1 Economics 420K (Microeconomic Theory) Second Midterm Examination University of Texas at Austin, Fall 2009 YOUR NAME: Instructions Write your name in the space at the top of this page. This is a closed-book examination. A calculator will be useful. There are seven pages. Check that you have all pages. Answer each question in the space provided. The examination is worth 50 points. Points are indicated in parentheses at the beginning of each question. Provide all the information asked for by each question. No credit will be given unless clearly demonstrated reasoning is shown. Partial credit will be given for work in the right direction. Question 1 (22 points) Consider a consumer who has preferences over two goods, x and y, represented by the following utility function: U(x,y) = 4xy 1.5 + 32 Let p x and p y denote prices and let I denote income. (a) (6 points) Use the method of Lagrange to derive complete expressions for the consumer’s demand for x and y at any prices and income. (You can get half points for using a method other than Lagrangeans.) (Further space for your answer on the following page.) 1

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2 (b) (4 points) Suppose that initially income is I=80 dollars, and prices are p x =4 and p y =10. Subsequently p y falls to 5. State the consumer’s optimal bundles (x,y) at the initial and final prices. Plot these bundles on an indifference-curve diagram with x on the horizontal
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Fall09MT2b - 1 Economics 420K(Microeconomic Theory Second...

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